Nonparametric pattern recognition algorithm for testing a hypothesis of the independence of random variables

A new method for testing a hypothesis of the independence of multidimensional random variables is proposed. The technique under consideration is based on the use of a nonparametric pattern recognition algorithm that meets a maximum likelihood criterion. In contrast to the traditional formulation of the pattern recognition problem, there is no a priori training sample. The initial information is represented by statistical data, which are made up of the values of a multivariate random variable. The distribution laws of random variables in the classes are estimated according to the initial statistical data for the conditions of their dependence and independence. When selecting optimal bandwidths for nonparametric kernel-type probability density estimates, the minimum standard deviation is used as a criterion. Estimates of the probability of pattern recognition error in the classes are calculated. Based on the minimum value of the estimates of the probabilities of pattern recognition errors, a decision is made on the independence or dependence of the random variables. The technique developed is used in the spectral analysis of remote sensing data.

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NONPARAMETRIC PATTERN RECOGNITION ALGORITHM IN TESTING HYPOTHESES ABOUT THE IDENTITY OF THE LAWS OF MULTDIMENSIONAL RANDOM VARIABLES DISTRIBUTION UNDER LARGE VOLUME OF STATISTICAL DATA

Informatika i sistemy upravleniya ◽

10.22250/isu.2020.64.103-112 ◽

2020 ◽

pp. 103-112

Author(s):

A.V. Lapko ◽

◽

V.A. Lapko ◽

Keyword(s):

Pattern Recognition ◽

Large Volume ◽

Statistical Data ◽

Random Variables ◽

Recognition Algorithm ◽

Pattern Recognition Algorithm ◽

Testing Hypotheses

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Formation of sets of independent components of a multidimensional random variable based on a nonparametric pattern recognition algorithm

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2021-9-3-9 ◽

2021 ◽

pp. 3-9

Author(s):

Aleksandr V. Lapko ◽

Vasiliy A. Lapko ◽

Anna V. Bakhtina

Keyword(s):

Pattern Recognition ◽

Random Variables ◽

Processing System ◽

Random Variable ◽

Recognition Algorithm ◽

Independent Random Variables ◽

Volume Data ◽

Independent Components ◽

Pearson Criterion ◽

Range Of Values

The possibility of circumventing the problem of decomposition of the range of values of random variables when testing various hypotheses is considered. A brief review of the literature on this problem is given. A method for forming sets of independent components of a multidimensional random variable is proposed, based on hypotheses testing about the independence of paired combinations of components of a multidimensional random variable. The method uses a two-dimensional non-parametric algorithm for pattern recognition of the kernel type, corresponding to the criterion of maximum likelihood. In contrast to the traditional method based on the application of the Pearson criterion, the proposed approach avoids the problem of decomposing the range of values of random variables into multidimensional intervals. The results of computational experiments performed according to the method of forming sets of independent random variables are presented. Using the information obtained, an information graph is constructed, the vertices of which correspond to the components of a multidimensional random variable, and the edges determine their independence. Then the vertices of the complete subgraphs correspond to groups of independent components of a random variable. The obtained results form the basis for the synthesis of a multi-level nonparametric large volume data processing system, each level of which corresponds to a specific set of independent random variables.

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